Study subjects have AML that has relapsed or recurred after their first course of treatment. A new treatment using an experimental drug called CMA-676 has been developed. This drug is an antibody joined to a potent chemotherapy agent. Since this particular antibody has shown in experiments to strongly adhere to leukemic cells it is hoped that leukemia can be selectively eliminated by this new agent. This drug is being evaluated to determine how effective it is in destroying leukemic cells in AML patients. In a previous study to test the safety of this drug, two out of 39- patients treated at various doses achieved a complete remission. These patients had advanced disease and were either unresponsive to treatment or had frequent recurrences of disease.